Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces

Dello Schiavo, Lorenzo; Suzuki, Kohei

Abstract

We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties for generalized intrinsic distances on strongly local Dirichlet spaces possibly without square field operator. We present many non-smooth and infinite-dimensional examples. As an application, we prove the integral Varadhan short-time asymptotic with respect to a given distance function for a large class of strongly local Dirichlet forms.

Citation

Dello Schiavo, L., & Suzuki, K. (2021). Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. Journal of Functional Analysis, 281(11), Article 109234. https://doi.org/10.1016/j.jfa.2021.109234

• Journal Article Type: Article
• Acceptance Date: Sep 4, 2021
• Online Publication Date: Sep 15, 2021
• Publication Date: 2021-12
• Deposit Date: Oct 20, 2024
• Journal: Journal of Functional Analysis
• Print ISSN: 0022-1236
• Electronic ISSN: 1096-0783
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 281
• Issue: 11
• Article Number: 109234
• DOI: https://doi.org/10.1016/j.jfa.2021.109234
• Public URL: https://durham-repository.worktribe.com/output/2977767
• Additional Information: This article is maintained by: Elsevier; Article Title: Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces; Journal Title: Journal of Functional Analysis; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.jfa.2021.109234; Content Type: article; Copyright: © 2021 Elsevier Inc. All rights reserved.